带轴向变形的柔顺机构多自由度伪刚体模型研究

发布时间：2019-06-03 01:02

【摘要】：柔顺机构是一种可以利用自身柔性构件的弹性变形来转换运动、力和能量的新型机构。与传统的刚性机构相比,由于它免去了运动副间的装配和摩擦磨损,因而表现出许多优点,近年来已成为国内外机构学领域的一个研究热点。柔顺机构具有独特的性能和广泛的应用前景,但是对于大变形造成的几何非线性导致柔顺机构的分析和设计变得非常困难。由Howell提出的伪刚体模型法将柔顺机构的非线性问题转化为等效刚性机构的线性问题来求解,为柔顺机构的研究奠定了基础。后来学者陆续提出了2R、PR伪刚体模型,但这些伪刚体模型自由度不足,导致其模拟精度和范围有限,限制了其进一步应用。针对上述问题,本文在现有模型的基础上,增加伪刚体模型的自由度,提出一种带轴向变形的多自由度PRR伪刚体模型,考虑多种复杂载荷情况,建立了相应的伪刚体新模型,并对该模型进行了相关研究。主要内容归纳如下:1、针对末端受力矩载荷时的柔顺杆,建立大变形柔顺机构的PRR伪刚体模型。将力矩载荷施加到模型的末端,采用参数近似化法建立模型特征半径系数的三维搜索过程,并对伪刚体模型中移动副引起的轴向位移占整个轴向移动的比例做定量分析。研究表明,在力矩载荷作用下,该移动副几乎不发生轴向位移,此时PRR模型与2R伪刚体模型基本一致。2、针对末端受力载荷的柔顺杆,建立大变形柔顺机构的PRR伪刚体模型。通过运动学正解得出模型特征参数的数值表达式,运用参数化近似法建立程序求解框图,运用线性回归法拟合模型的刚度系数。利用数值分析软件,通过与现有伪刚体模型以及柔顺杆的末端轨迹特征进行分析对比,表明PRR伪刚体模型的模拟精度进一步提高。3、针对末端受复合载荷形式的柔顺杆,建立大变形柔顺机构的PRR伪刚体模型。将载荷比进行极端化处理,推导出两种极端载荷形式下伪刚体模型的数学表达式。通过建立三维搜索程序和线性拟合方法求解出模型的特征参数,通过与其他模型对比分析验证了受复合载荷时PRR模型的优越性。4、将受不同载荷时的PRR伪刚体模型应用到平面柔顺机构中,建立柔顺四杆机构和柔顺曲柄-滑块机构的PRR伪刚体模型,通过力-变形分析得出滑块位移和曲柄转角关系的曲线图及柔顺四杆机构中柔顺杆末端的位姿变化图,通过与有限元分析结果对比,验证了PRR伪刚体模型在实际柔顺机构应用中的有效性。
[Abstract]:Compliance mechanism is a new type of mechanism which can transform motion, force and energy by using the elastic deformation of its own flexible components. Compared with the traditional rigid mechanism, it has shown many advantages because it eliminates the assembly and friction and wear between moving pairs, so it has become a research hot spot in the field of mechanism at home and abroad in recent years. Compliant mechanism has unique performance and wide application prospect, but it is very difficult to analyze and design compliant mechanism because of geometric nonlinear caused by large deformation. The pseudo-rigid body model method proposed by Howell converts the nonlinear problem of compliant mechanism into the linear problem of equivalent rigid mechanism, which lays a foundation for the research of compliant mechanism. Later, scholars put forward 2R, PR pseudo-rigid body model one after another, but these pseudo-rigid body models have insufficient degree of freedom, which leads to the limited simulation accuracy and range, which limits its further application. In order to solve the above problems, a multi-degree-of-freedom PRR pseudo-rigid body model with axial deformation is proposed by adding the degrees of freedom of the pseudo-rigid body model on the basis of the existing models. Considering a variety of complex loads, a new pseudo-rigid body model is established. The model is also studied. The main contents are summarized as follows: 1. The PRR pseudo-rigid body model of large deformation compliance mechanism is established for the compliant rod loaded with moment at the end. The torque load is applied to the end of the model, and the three-dimensional search process of the characteristic radius coefficient of the model is established by using the parameter approximate method, and the proportion of the axial displacement caused by the moving pair in the pseudo-rigid body model to the whole axial movement is quantitatively analyzed. The results show that the axial displacement of the moving pair almost does not occur under torque load, and the PRR model is basically consistent with the 2R pseudo-rigid body model. 2, the PRR pseudo-rigid body model of large deformation compliant mechanism is established for the compliant rod loaded at the end of the force. The numerical expression of the characteristic parameters of the model is obtained by the forward kinematic solution, the program block diagram is established by using the parametric approximate method, and the stiffness coefficient of the model is fitted by the linear regression method. By using the numerical analysis software, the simulation accuracy of the PRR pseudo-rigid body model is further improved by comparing with the existing pseudo-rigid body model and the end trajectory characteristics of the compliant rod. 3, for the compliant rod in the form of composite load at the end, The PRR pseudo-rigid body model of large deformation compliant mechanism is established. The load ratio is extreme treated, and the mathematical expressions of the pseudo-rigid body model under two extreme load forms are derived. The characteristic parameters of the model are solved by establishing three-dimensional search program and linear fitting method, and the superiority of PRR model under compound load is verified by comparing with other models. The PRR pseudo-rigid body model under different loads is applied to the plane compliant mechanism, and the PRR pseudo-rigid body model of compliant four-bar mechanism and compliant crank-slider mechanism is established. Through force-deformation analysis, the curve diagram of the relationship between slider displacement and crank angle and the pose change diagram at the end of flexible four-bar mechanism are obtained, and the results are compared with those of finite element analysis. The effectiveness of PRR pseudo-rigid body model in practical compliance mechanism is verified.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TH112

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